Example 9.2. Figure 9.2 shows the one-line diagr Generators are connected at bus
ID: 2266315 • Letter: E
Question
Example 9.2. Figure 9.2 shows the one-line diagr Generators are connected at buses and while loads are indicated atall re 9.2 shows the one-line diagram of a simple power system. buses. Base values for the transmission system are 100 MVA four data of Table 9.2 give per-unit series impedances and line-charging susceptances for the nominal-r equivalents of the four lines identified by the buses at which they terminate. The bus data in Table 9.3 list values for P, Q, and V at each bus. The Q values of load are calculated from the corresponding P values assuming a power factor of 0.85. The net scheduled values, P, sch and Q,sch, are neg the load buses and . Generated Qgi is not specified where voltage 230 kV. The line ative at Birch Elm Maple Pine FIGURE 9.2 One-line diagram for Example 9.2 showing the bus names and numbers.Explanation / Answer
%------Newton Raphson load flow program for any bus system------------
clc
clear all
load linedata4.m %calling line data....
A=linedata4; %getlinedata to some variable...
nb=A(1,1); % bus number...
itr=A(1,2); %max iteration taken...
rtr=A(1,3); %regulating transformers taken...
nrtr=A(1,4); %non-regulating transformers taken...
trl=A(1,5); % no. of transmission lines...
sz=A(1,6); %no. of shunt impedances...
pq=A(2,1); %no. of load buses....
g=A(2,2); %no. of generator buses...
tol=A(2,3); %tolerance taken...
nl=rtr+trl+nrtr; %total no. of transmission lines...
m11=nl+2+sz;
Ld=A(nl+sz+3:m11+pq,:); %load data...
Gd=A(nl+sz+pq+3:m11+pq+g,:); %generator data...
for i=1:nl
sb(i)=A(i+2,1); % From bus number...
rb(i)=A(i+2,2); % To bus number...
R(i)=A(i+2,3); %line resistance
X(i)=A(i+2,4); %line reactance...
B(i)=A(i+2,6)/2; %line suseptance...
bx(i)=complex(0,B(i));
TP(i)=A(i+2,7); %line tapping...
Z(i)=complex(R(i),X(i)); %line impedance...
y(i)=1/Z(i); %line admittance...
end
ybus=zeros(nb,nb);
% ------------FORMATION OF YBUS MATRIX-------------
% ------------OFF diagonal elements------------
for i=1:nl
ybus(sb(i),rb(i))=ybus(sb(i),rb(i))-y(i)/TP(i);
ybus(rb(i),sb(i))=ybus(sb(i),rb(i));
end
ybus;
% --------------diagonal elements------------
for k1=1:nb
for i=1:nl
if sb(i)==k1
ybus(k1,k1)=ybus(k1,k1)+y(i)/(TP(i)^2)+bx(i);
else if rb(i)==k1
ybus(k1,k1)=ybus(k1,k1)+y(i)+bx(i);
end
end
end
end
ybus;
Y1=zeros(nb,nb);
%--------------shunt impedance data-------------
s=A(nl+3:m11,:);
sh=s(:,1);
for j=1:sz
if ((sz~=0)&(s(j,1)==sh(j,1)))
Y1(sh(j,1),sh(j,1))=Y1(sh(j,1),sh(j,1))+1/complex(s(j,3),s(j,4));
end
end
Y1;
if sz~=0
y1=[ybus+Y1];
else
y1=ybus;
end
y1;
G=real(y1);
B1=imag(y1);
Y=abs(ybus);
YA=angle(ybus);
%---------------UNKNOWN VOLTAGE MAGNITUDES-------------
VM=ones(nb,1);
for ii=1:g
%if Gd(k,1)==gd(k,1)
VM(ii)=A(ii+m11+pq,5);
%end
end
VM;
%---------------UNKNOWN VOLTAGE angles-------------
DL=zeros(nb,1);
YGG=y1(1:g,1:g);
YGL=y1(1:g,g+1:nb);
YLG=y1(g+1:nb,1:g);
YLL=y1(g+1:nb,g+1:nb);
YLL1=inv(YLL);
FLG=-YLL1*YLG;
%--------------iteration starts-------------
iter=0
while iter<=0.0001
%------------calculation of inected powers---------
Pcal=zeros(nb,1);
Qcal=zeros(nb,1);
for l=1:nb
for k1=1:nb
Pcal(l) = Pcal(l) + VM(l)* VM(k1)*(G(l,k1)*cos(DL(l)-DL(k1)) + B1(l,k1)*sin(DL(l)-DL(k1)));
Qcal(l) = Qcal(l) + VM(l)* VM(k1)*(G(l,k1)*sin(DL(l)-DL(k1)) - B1(l,k1)*cos(DL(l)-DL(k1)));
end
end
Pcal;
Qcal;
%------------Mismatch Calculation------------------------------------------
Ps=zeros(nb,1);
% % bl=L1(:,1);
% % bg=G1(:,1);
bl=Ld(:,1);
for ii=1:g
Ps(ii)=Ps(ii)+Gd(ii,2);
end
for pq1=1:pq
Ps(bl(pq1))=Ps(bl(pq1))-Ld(pq1,2);
end
Qs=zeros(nb,1);
for pq1=1:pq
Qs(bl(pq1))=Qs(bl(pq1))-Ld(pq1,3);
end
Ps;
Qs;
for l=1:nb
DP(l)=Ps(l)-Pcal(l);
DQ(l)=Qs(l)-Qcal(l);
end
DP;
DQ;
DPA=DP(2:nb);
DQA=DQ(g+1:nb);
DPQ=[DPA';DQA'];
if max(abs(DPQ))<=0.0001
disp('----------------converged------------------')
Pcal
Qcal
VM
DL
Ploss=sum(Pcal)
Qloss=sum(Qcal);
Ygb2=zeros(nb,nb);
%-------------required power flow---------------
for xk=1:nl
Ygb2(sb(xk),rb(xk))=bx(xk);
Ygb2(rb(xk),sb(xk))=Ygb2(sb(xk),rb(xk));
end
Ygb2;
g2=real(Ygb2);
b2=imag(Ygb2);
for pk=1:nb
for qk=1:nb
if pk~=qk
PF(pk,qk)=-VM(pk)*VM(pk)*Y(pk,qk)*cos(YA(pk,qk))+VM(pk)*VM(qk)*Y(pk,qk)*cos(DL(pk)-DL(qk)-YA(pk,qk));
QF(pk,qk)=VM(pk)*VM(pk)*Y(pk,qk)*sin(YA(pk,qk))+VM(pk)*VM(qk)*Y(pk,qk)*sin(DL(pk)-DL(qk)-YA(pk,qk))-VM(pk)*VM(pk)*b2(pk,qk);
end
end
end
PF
QF
LF1=complex(PF,QF);
LF=abs(LF1);
% -----------voltage stability index--------
for l=1:nb
VMC(l)=complex(VM(l)*cos(DL(l)),VM(l)*sin(DL(l)));
end
VMC;
F2=zeros(nb,1);
for p1=g+1:nb
for ii=1:g
F2(ii)=F2(ii)+FLG(p1-g,ii)*VMC(ii)/VMC(p1);
end
F1(p1)=sum(F2(p1));
L(p1)=1-F1(p1);
L1(p1)=abs(L(p1));
end
L1;
break
else
%-----------------Formation of Jacobian Matrix-----------------------------
% %---------- formation of J1 MATRIX---------
% % ----------diagonal elements---------
for t1 =2:nb
DPDD(t1,t1)=-Qcal(t1)-B1(t1,t1)*VM(t1)*VM(t1);
end
% % ---------OFF diagonal elements---------
for m1=2:nb
for n1=2:nb
if m1~=n1
DPDD(m1,n1)=VM(m1)*VM(n1)*(G(m1,n1)*sin(DL(m1)-DL(n1))-B1(m1,n1)*cos(DL(m1)-DL(n1)));
end
end
end
% %----------- formation of J2 MATRIX----------
% % diagonal elements----------
for t2=g+1:nb
DPDVM(t2,t2)=Pcal(t2)/VM(t2)+G(t2,t2)*VM(t2);
end
% ----------OFF diagonal elements---------
for m2=2:nb
for n2=g+1:nb
if m2~=n2
DPDVM(m2,n2)=VM(m2)*(G(m2,n2)*cos(DL(m2)-DL(n2))+B1(m2,n2)*sin(DL(m2)-DL(n2)));
end
end
end
% --------formation of J3 MATRIX----------
% ------diagonal elements-----------
for t3 =g+1:nb
DQDD(t3,t3)=Pcal(t3)-G(t3,t3)*VM(t3)*VM(t3);
end
% --------OFF diagonal elements-----------
for m3=g+1:nb
for n3=2:nb
if m3~=n3
DQDD(m3,n3)=-VM(m3)*VM(n3)*(G(m3,n3)*cos(DL(m3)-DL(n3))+B1(m3,n3)*sin(DL(m3)-DL(n3)));
end
end
end
% ----------formation of J4 MATRIX-------------
% ----------diagonal elements---------
for t4 =g+1:nb
DQDVM(t4,t4)=Qcal(t4)/VM(t4)-B1(t4,t4)*VM(t4);
end
% ----------OFF diagonal elements-----------
for m4=g+1:nb
for n4=g+1:nb
if m4~=n4
DQDVM(m4,n4)=VM(m4)*(G(m4,n4)*sin(DL(m4)-DL(n4))-B1(m4,n4)*cos(DL(m4)-DL(n4)));
end
end
end
J1=DPDD(2:nb,2:nb);
J2=DPDVM(2:nb,g+1:nb);
J3=DQDD(g+1:nb,2:nb);
J4=DQDVM(g+1:nb,g+1:nb);
J=[J1 J2;
J3 J4];
JI=inv(J);
DDDV=JI*DPQ;
%DDL=zeros(nb,1);
%DVM=zeros(nb,1);
DDL=DDDV(1:nb-1);
DVM=DDDV(nb:2*(nb)-1-g);
for a=1:nb-1
DL(a+1)=DL(a+1)+DDL(a);
end
for b=1:nb-g
VM(b+g)=VM(b+g)+DVM(b);
end
DL;
VM;
end
iter=iter+1
end
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.